Chaotic dynamics from interspike intervals

A N Pavlov; Olga Sosnovtseva; Erik Mosekilde; V S Anishchenko

Chaotic dynamics from interspike intervals

A N Pavlov, Olga Sosnovtseva, Erik Mosekilde, V S Anishchenko

Renal and Vascular Research

25 Citations (Scopus)

Abstract

Considering two different mathematical models describing chaotic spiking phenomena, namely, an integrate-and-fire and a threshold-crossing model, we discuss the problem of extracting dynamics from interspike intervals (ISIs) and show that the possibilities of computing the largest Lyapunov exponent (LE) from point processes differ between the two models. We also consider the problem of estimating the second LE and the possibility to diagnose hyperchaotic behavior by processing spike trains. Since the second exponent is quite sensitive to the structure of the ISI series, we investigate the problem of its computation.

Original language	English
Journal	Physical Review E (Statistical, Nonlinear, and Soft Matter Physics)
Volume	63
Issue number	3 Pt 2
Pages (from-to)	036205
ISSN	1539-3755
Publication status	Published - 1 Mar 2001

Cite this

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title = "Chaotic dynamics from interspike intervals",

abstract = "Considering two different mathematical models describing chaotic spiking phenomena, namely, an integrate-and-fire and a threshold-crossing model, we discuss the problem of extracting dynamics from interspike intervals (ISIs) and show that the possibilities of computing the largest Lyapunov exponent (LE) from point processes differ between the two models. We also consider the problem of estimating the second LE and the possibility to diagnose hyperchaotic behavior by processing spike trains. Since the second exponent is quite sensitive to the structure of the ISI series, we investigate the problem of its computation.",

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T1 - Chaotic dynamics from interspike intervals

AU - Pavlov, A N

AU - Sosnovtseva, Olga

AU - Mosekilde, Erik

AU - Anishchenko, V S

PY - 2001/3/1

Y1 - 2001/3/1

N2 - Considering two different mathematical models describing chaotic spiking phenomena, namely, an integrate-and-fire and a threshold-crossing model, we discuss the problem of extracting dynamics from interspike intervals (ISIs) and show that the possibilities of computing the largest Lyapunov exponent (LE) from point processes differ between the two models. We also consider the problem of estimating the second LE and the possibility to diagnose hyperchaotic behavior by processing spike trains. Since the second exponent is quite sensitive to the structure of the ISI series, we investigate the problem of its computation.

AB - Considering two different mathematical models describing chaotic spiking phenomena, namely, an integrate-and-fire and a threshold-crossing model, we discuss the problem of extracting dynamics from interspike intervals (ISIs) and show that the possibilities of computing the largest Lyapunov exponent (LE) from point processes differ between the two models. We also consider the problem of estimating the second LE and the possibility to diagnose hyperchaotic behavior by processing spike trains. Since the second exponent is quite sensitive to the structure of the ISI series, we investigate the problem of its computation.

M3 - Journal article

C2 - 11308739

SN - 2470-0045

VL - 63

SP - 036205

JO - Physical Review E

JF - Physical Review E

IS - 3 Pt 2

ER -

Chaotic dynamics from interspike intervals

Abstract

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